A more likely spelling would be BUNKOWSKI.

An Emilie Bunkowski, age 18, departed Hamburg, 21 Apr 1901, bound for New York. Her prior residence was Klokock and her ethnicity was Russian. The ship was the S.S. Batavia. It arrived in New York, 5 May 1901. She was on her way to see her uncle, Aug. Bunkosky, in Olean, Cattaraugus Co., NY. So although the name is similar, her destination was not Michigan. Another young woman of the same name, age 17, departed Hamburg, 13 Mar 1901, on the S.S. Taormina, arriving in New York, 1 Apr 1901, but under the spelling “Bunkowsky” (indexed as “Buchinsky” on Ancestry). In the arrival list she appears to be accompanied by Ludwig Bunkowsky, age 19. But again, their destination is different, Schenectady, NY, to see their uncle, Adolf S*.